Seminar Event Detail


Applied Interdisciplinary Mathematics (AIM)

Date:  Friday, February 27, 2015
Location:  1084 East Hall (3:00 PM to 4:00 PM)

Title:  A population density approach with particles

Abstract:   According to the population density approach, instead of tracking the state of each oscillator in a large population as they evolve according to ordinary differential equations, one may consider the primary variable of interest to be the population density over state space. After accounting for additive Gaussian noise and coupling within the population, the population density is governed by a non-linear and non-local integro-advection-diffusion differential equation. When the state space has many dimensions, it appears that nothing has been gained by trading a large number of state variables for a differential equation with a large number of dimensions. We exploit the fact that the population of limit cycle oscillators, or even chaotic oscillators, occupy only a small amount of the state space. An efficient numerical method for solving the governing equation for the population density results from discretizing over particles in a grid free approach and utilizing a diffusion velocity method. We are thus permitted to study the dynamics of a population of noisy coupled oscillators without having to resort to dimension reduction strategies. We can consider detailed oscillator models involving physical variables. In this talk, I will detail our numerical method and present its application to a model of a population of neurons and a population of coupled biochemical oscillators.

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Speaker:  Adam Stinchcombe
Institution:  University of Michigan

Event Organizer:   AIM Seminar Organizers    millerpd@umich.edu

 

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